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### 2023年美赛特等奖论文-E-2307336-解密 #### 大学生数学建模与美国大学生数学建模竞赛(MCM/ICM) 在2023年的美国大学生数学建模竞赛(MCM/ICM)中，编号为E-2307336的团队凭借其出色的数学模型和解决方案获得了特等奖(O奖)。这篇论文主要关注的是光污染问题，并提出了一系列创新的方法来评估和减轻光污染的影响。 #### 光污染风险评估模型对于任务1，研究团队提出了一个综合性的“光污染风险评估模型”。该模型考虑了四个维度的风险因素：人类、野生动物、植物以及由光污染造成的能源浪费。为了更准确地评估这些因素的影响程度，模型采用了扩展权重多指标排序技术(EWM-TOPSIS)，这是一种能够处理多个指标并给出总体风险评分的有效方法。根据评分结果，可以将地点的风险水平划分为四个等级：脆弱(0-1)、较差(1-2)、一般(2-3)和良好(3-4)。 #### 四个典型区域的应用案例在任务2中，研究团队将这个光污染风险评估模型应用于深圳市的四个典型区域：城市区、郊区、乡村以及保护区。通过收集夜间遥感数据和多光谱遥感数据，研究者计算了这些区域的归一化植被指数(NDVI)、夜间辐射强度以及人口密度等关键指标。根据这些数据，保护区的风险评分为0.357992，乡村社区的风险评分为1.859474，郊区社区的风险评分为2.114942，而城市社区的风险评分为3.19662。这些评分分别对应于脆弱、较差、一般和良好的风险等级。 #### 干预策略与模型建立为了进一步解决光污染问题，在任务3中，研究团队开发了三种干预策略：改善光源、降低照明强度以及优化区域灯光布局。每种策略都包含了一系列具体行动方案。基于微分方程的干预策略模型被用来量化这些策略对降低风险等级的具体影响。 - **改善光源**：这包括使用更环保的LED灯取代传统的白炽灯或荧光灯，以减少能源消耗和环境污染。 - **降低照明强度**：通过调整照明设备的设计和设置，例如使用智能控制系统，可以根据实际需求动态调节照明强度，避免过度照明。 - **优化区域灯光布局**：通过对城市规划进行调整，合理安排公共照明设施的位置和数量，以最小化对自然环境的影响。 #### 模型验证与未来展望在任务4中，研究团队可能会继续探讨如何验证这些干预策略的有效性，并对未来可能遇到的问题提出解决方案。例如，可以通过模拟不同场景下的光污染情况来评估模型的预测能力，或者研究如何将这些理论应用到其他城市和地区中去。这篇特等奖论文不仅展示了数学建模在解决现实世界问题中的强大作用，还提供了一套系统性的方法来应对光污染这一全球性挑战。通过采用科学的方法和技术手段，我们可以更好地保护地球上的生态环境，创造一个更加可持续的未来。

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Problem Chosen

2023

MCM/ICM

Summary Sheet

Team Control Number

2307336

Protect the Night, Control the Light!

Summary

People generally are struck by the ’beauty’ of city lights without realizing that these

are also images of pollution, like admiring the beauty of the rainbow colours that gaso-

line produces in water and not recognising that it is chemical pollution. In this paper,

we construct a broadly applicable Light Pollution Risk Assessment Model to assess the

risk level of a given location, and propose an Intervention Strategy Model to mitigate

the effects of light pollution in various locations.

For Task 1, we propose a Light Pollution Risk Assessment Model. The model

integrates risks from four dimensions: humans, wildlife, plants, and energy waste

caused by light pollution. Considering multiple related indicators, EWM-TOPSIS is

applied to solve the overall risk score, which is divided into four levels: fragile(0-1),

poor(1-2), ordinary(2-3), and good(3-4).

For Task 2, the Light Pollution Risk Assessment Model is applied to four typical

regions in Shenzhen, representing urban, suburban, rural, and protected areas. In the

data preparation phase, we use nighttime remote sensing and multi-spectral remote

sensing data to estimate the Normalized Difference Vegetation Index (NDVI), night-

time radiance, and population density in the study areas. The protected area has a risk

score of 0.357992, while the rural community has a risk score of 1.859474, the subur-

ban community has a risk score of 2.114942, and the urban community has a risk score

of 3.19662. These scores correspond to the fragile, poor, ordinary, and good levels,

respectively.

For Task 3, we develop three intervention strategies including improving the light

source, lowering the lighting intensity and optimizing regional light layouts. Then

we list multiple speciﬁc actions for each strategy. Intervention Strategy Model based

on Differential Equation is established to quantify how three strategies impact the

risk level.

For Task 4, we select urban and suburban communities to verify the effectiveness

of the three intervention strategies. Over the next 50 years, the risk scores after the

implementation of the three strategies are reduced by approximately 2%, 6%, and 3%

respectively. It can be concluded that the second strategy, lowering the lighting in-

tensity that aims to reduce the total amount of light radiance is the most effective

intervention strategy for both urban and suburban areas.

Finally, the sensitivity analysis of the risk assessment model shows that the ﬂuctua-

tion of a single evaluation indicator by -10% - 10% has a reasonable impact on the ﬁnal

risk score shown in Figure 16. Therefore, the model is robust to changes in a single

indicator. Besides, the sensitivity analysis of the Strategy Model shown in Figure 17

means that our model is robust to the growth rate.

Keywords: Light Pollution; Intervention strategies; EWM-TOPSIS; Differential Equa-

tion

Team # 2307336 Page 2 of 24

Contents

1 Introduction 3

1.1 Problem Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Restatement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Our Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Assumptions and Explanations 4

3 Notations 5

4 Task 1: Regional Light Pollution Risk Level Metric 6

4.1 Problem Description and Analysis . . . . . . . . . . . . . . . . . . . . . . 6

4.2 Indicator selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.3 Light Pollution Risk Evaluation Model based on EWM-TOPSIS . . . . . 8

4.3.1 EWM-TOPSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.3.2 Model establishment . . . . . . . . . . . . . . . . . . . . . . . . . . 10

5 Task 2: Metric Application and Result Interpretation 11

5.1 Data Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5.2 Metric Application and Result Interpretation . . . . . . . . . . . . . . . . 13

6 Task 3: Intervention Strategies and Speciﬁc Actions 14

6.1 Strategy 1: Improve the light source . . . . . . . . . . . . . . . . . . . . . 14

6.2 Strategy 2: Lower the lighting intensity . . . . . . . . . . . . . . . . . . . 16

6.3 Strategy 3: Optimize regional lighting layouts . . . . . . . . . . . . . . . 17

7 Task 4: Strategy Determination and Impacts Evaluation 18

7.1 Strategy Implementation and Impacts Evaluation . . . . . . . . . . . . . 18

7.2 Strategy Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

8 Sensitivity Analysis 20

8.1 Evaluation model sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 20

8.2 Strategy model sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

9 Strength and Weakness 21

9.1 Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

9.2 Weakness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

10 Conclusion 22

11 Flier 23

References 24

Team # 2307336 Page 3 of 24

1 Introduction

1.1 Problem Background

Looking at the International Space Station’s images of the Earth at night, people

generally are struck by the ’beauty’ of city lights, as if they were lights on a Christmas

tree, without realizing that these are also images of pollution. It is like admiring the

beauty of the rainbow colours that gasoline produces in water and not recognising that

it is chemical pollution.

The inappropriate or excessive use of artiﬁcial light, known as light pollution, can

have serious environmental consequences for humans, wildlife, and our climate. Com-

ponents of light pollution include:

• Light trespass: light falling where it is not intended or needed

• Over-illumination: lighting intensity higher than that which is appropriate

• Light cluster: bright, confusing and excessive grouping of light sources

The impacts of light pollution can be far-reaching and varied, affecting both natural

and human systems. There is a growing body of evidence that links light pollution to

measurable negative impacts on human health, wildlife, and the environment. Some

examples of these negative impacts include:

• Harming human health and effecting crime and safety

• Disrupting the ecosystem and wildlife

• Increasing energy consumption

• Affecting astronomical observations

It is important to understand these impacts and to take steps to mitigate them to

minimize the negative effects on our environment, health, and economy. There’s a lot

of room for improvement - if we light more carefully, we should be able to reduce

negative inﬂuences, whilst still lighting the ground.

There are several intervention strategies that can be employed to address light pol-

lution, such as using shielded, directional and energy-efﬁcient lighting, enacting light-

ing ordinances and implementing lighting curfews etc.

(a) Image taken from the International Space

Station. (Image credit: NASA)

(b) Light trespass falls where it is not needed. (Image

credit: Twitter @St Brian)

Figure 1: Light Pollution Display

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